An analysis of control structures for modular multilevel converters (MMCs) used in high-voltage direct current (HVDC) applications is addressed. In particular, this paper focuses on the case of a point-to-point link with master-slave control, considering an energy-based scheme (also known as closed loop or energy controlled) for the MMC, meaning that the internal energy of the converter is explicitly controlled. With such an approach, the MMC internal energy can be controlled independently of the energy of the HVDC link, and whereas the internal capacitance of the MMC depends on the converter's rating, the capacitance at the dc terminal depends on the cable length. Therefore, several possibilities regarding the outer control structure (internal energy and dc voltage) arise, affecting the overall dynamics differently. Whereas for a long link, the classic control structures should perform well, for shorter links the transient performance might not be acceptable and other alternatives shall be used instead. Different control structures are presented and evaluated in this paper through small-signal and frequency-domain analysis, and validated through time-domain simulation with MATLAB Simscape Power Systems.